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Automated computation of robust normal forms of planar analytic vector fields

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  • We construct an auto-validated algorithm that calculates a close to identity change of variables which brings a general saddle point into a normal form. The transformation is robust in the underlying vector field, and is analytic on a computable neighbourhood of the saddle point. The normal form is suitable for computations aimed at enclosing the flow close to the saddle, and the time it takes a trajectory to pass it. Several examples illustrate the usefulness of this method.
    Mathematics Subject Classification: Primary: 34C20, Secondary: 37M99, 65L70, 65G20.


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